X-ray crystal monochromator with a reflecting surface that conforms to part of a logarithmic spiral



P" 1969 w. K. DE JONGH X-RAY CRYSTAL MONOCHROMATOR WITH A THAT CONFORMS TO PART oF' A LOGARITHMIC SPIRAL Filed Sept. 5, 1965 FIGS FIGS

INVENTOR. WILHELMUS K. DE: JONGH AGE United States Patent US. Cl. 250-515 4 Claims ABSTRACT OF THE DISCLOSURE A crystal monochromator for diflracting X-rays which is in the form of an elongated strip bent so that its surface is part of a logarithmic spiral. The elongated strip may be a single crystal, or flexible carrier material such as sheet steel laminated with substances which reflect X-rays.

This invention relates to a device for making a spectrochemical analyses with X-rays, and in particular to an analyzing crystal which is used in a device employing X-rays for making spectrochernical analyses.

Spectrochemical analyses with X-rays is based on the diffraction of X-rays through crystals. Thus, any crystal will ditfract X-rays in accordance with Braggs Law which states:

A set of lattice planes of the crystal lattice, with mutual distance d, will be capable of reflecting the X-ray beam with Wavelength A only at angles of incidence 0 which satisfies this equation.

In a device for making a spectrochemical analysis using X-rays an analyzer is employed which generally has the shape of an elongated strip consisting of a single crystal plate provided with parallel surfaces. This plate will hereinafter be termed the plate of incidence ifOI X-rays. When the plate of incidence for X-rays of a given wavelength is arranged at the correct angle 0, rays originating from a source of a small cross-section will be reflected by a given zone of the plate of incidence. When using a flat plate of incidence only a small part of the incident rays is reflected. In order to use a wider beam of the emitted radiation, a focusing arrangement is used in which the reflecting surface of the plate of incidence is curved. The most favorable arrangement is obtained by bending the plate of incidence in the form which corresponds to the curvature of the logarithmic spiral. This shape of the plate of incidence enables the active surface used for the X-ray deflection, to be as large as possible. Furthermore, rays starting from a source of finite, although none too large proportions, and of a given wavelength can be collected in a sharply bounded focus after reflection. As a result of this a high intensity of the reflected radiations is obtained.

Actually the plate of incidence is an X-ray monochromator which need not necessarily consist of a single crystal. It may be a carrier which is coated with a material which reflects the radiation. In that case the carrier has a surface curved to the desired shape.

When using thin rectangular crystal plates, the required shape can be obtained by clamping the plate between two moldings which are curved in the correct manner. In another solution having the advantage that the curvature is adjustable, the ends of a rectangular crystal plate are clamped in a holder of such a construction that unequal bending moments can be exerted on the two ICC ends. The resulting curvature of the crystal plate is a good approximation of the logarithmic spiral and the shape can easily be adapted to various distances between the ray source and the plate of incidence.

The invention relates to a plate of incidence or crystal monochromator for X-ray diffraction which has the shape of an elongated strip, which strip, when deflected, assumes the shape of a part of a logarithmic spiral. According to the invention the surface of the plate of incidence is bounded by four sides joining one another, two opposite points of intersection of which are located on a symmetry line of the surface. The remaining two points of intersection determine the largest width of the strip. Furthermore the sides which meet in one point of intersection with the symmetry line are curved concave with respect to the said line, and the sides which meet in the opposite point of intersection are curved convex with respect to the said line. Such a plate of incidence may be made from flexible single crystal plates, bounded by parallel surfaces, but may alternatively consist of flexible carrier material, for example, thin sheet steel which is laminated with substances which reflect X-rays.

The invention will now be described in greater detail with reference to the accompanying drawing, in which:

FIG. 1 shows the arrangement for an X-ray spectrometer with logarithmically curved plate of incidence.

FIG. 2 diagrammatically shows the manner of deflection of the plate of incidence.

FIGS. 3 and 4 show embodiments of plates of incidence according to the invention.

FIG. 5 shows a mounting structure for supporting a deflection plate of incidence.

The logarithmic spiral has the characteristic feature that any radius vector from the origin 0 encloses equal angles with the surface of the curve A-B, as a result of which the origin 0 also is the focus of reflected rays of equal wavelengths.

The radius of curvature in any point of the curve A-B diifers from the radii of curvature in adjacent points but these radii have the common property that they are the diameters of circles passing through the origin 0. Therefore, the radii of curvature are determined by R=OB/sin 0 Starting from the radius vector r through point P the radius vector through an adjacent point is r=rd+r d cotan 0 wherein x is the distance between two points of incidence,

r d =x sin 0 The general equation for the radius of curvature of deflection lines of small curvature is:

S=l/Y" (8) wherein Y" is the second diflerential coeflicient of the curve A deflection line of this type is found in a carrier which is loaded between two supporting points located at the ends. In a slightly curved strip-shaped plate of equal thickness, it can be shown that wherein M is the bending moment in any cross-section, J the moment of inertia at that point and E the modulus of elasticity.

For a rectangular cross-section M P 3% for x e e and between the pressure point P and the support point 0 M =P (Bx) for x z 0 12 In order that the curve of bending have the same shape as the logarithmic spiral, it :follows from (9) that and it further follows:

a =A(lx/B) (Li- 2 for x and wherein A is the largest width of the strip.

The shape of a strip-shaped plate shown in FIG. 3 results from these equations.

When such a plate is used, a deflection is possible such that diffraction X-rays the wavelength of which satisfies Braggs formula for a given angle 6, takes place without aberration. This adjustment can be found in a comparatively simple manner. It is assumed that the ends of the plate of incidence are clamped in sliding members of a holder movable at right angles to the surface. This holder also comprises fixed stop members against which the plate of incidence engages at both sides of the symmetry line at the area of the largest width. Radiation which is reflected by the plate of incidence and which has the wavelength for which the angle 0 is associated which has been taken into account in shaping the plate of incidence is received on a fluorescent screen which is provided at the area of the focus. By moving the sliding members, the curvature can be varied and adjustment can be found at which the definition of the focusing is largest.

It would be cumbersome, however, if [for every wavelength a separate plate of incidence had to be used as it follows from the Equations 14 and 15 that a the local width of the crystal, depends upon the reflection angle 6. Except for the angle 0 for which the shape fully satisfies the logarithmic shape, other angles 6 involve some aberration. For an admissible aberration an angular range on either side of 0 within narrow limits may be considered a useful working range. It has been found that the aberration increases more rapidly when the associated reflection angle for rays of other wavelengths is larger than when the said angle is smaller than the angle 0,. For a plate of incidence consisting of mica, it has been found that the shape which satisfies an angle of incidence for the rays of which cos 0 =0.9 is the most favorable for use as a monochromator for rays of which the reflection angle varies bet-ween 0 and 30. The greatest aberrations occur at 1445 and 30 and are equal to one another.

In addition to mica all other known materials suitable for reflection crystals which can be curved for making a plate of incidence according to the invention, may be considered.

If the plate of incidence is used as a carrier for the reflecting layer, substances may be used which are provided in thin layers on the surface and have properties useful for the reflection of rays.

The arrangement of the ends of a strip of material which tapers to points may present difliculties when the plate has a low mechanical strength. Since the ends of the plate of incidence do not contribute substantially to the reflection of rays, the plate of incidence may be extended at the ends as shown in FIG. 4, by laterally projecting wings which afford the required rigidity to the supported parts.

X-rays from a source 1 are deflected by a monochromator 2, which is an elongated strip of a flat crystal plate the central portion of which bears against two upright right angle members 3 of a rectangular frame 4 while the end portions rest on contact members the height of which is adjustable by screws 5 so that by turning knobs 6 the ends of the strip may be raised. The deflected X-rays are received by a counter 7.

While the invention has been described in connection with specific examples and applications thereof, other modifications will be apparent to those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

What is claimed is:

1. An X-ray crystal monochromator, the reflecting surface of which is curved in the shape of parts of a logarithmic spiral the smallest radius of curvature of which is adapted to be placed closest to the source of X-rays by bending an elongated strip of a flat crystal plate having a central portion and end portions, the opposite end portions of which are deflected in the same direction with respect to the central portion, which strip is bounded by four sides joining one another in pairs, two opposite points of intersection of said sides being located at the end portions and the remaining two points of intersection being located in the central portion and determining the largest width of the strip, said sides meeting in one point of intersection at the end portion placed closest to the source being curved concave with respect to the central portion and the sides which meet in the opposite point of intersection being curved convex with respect to the central portion of the strip.

2. An X-ray crystal monochromator as claimed in claim 1, in which the sides are curved in one direction from the largest width according to the equation and in the other direction according to the equation wherein A is the largest width, B and 5B the length of the strip on one side an on the other side respectively of the largest width, r is the average focus distance, 0 the diffraction angle and X is measured positive and negative respectively from the largest width in both directions.

3. An X-ray crystal monochromator as claimed in claim 2, in which the monochromator is constituted of mica, and the elongated strip has a shape such that upon deflection the curvature of the strip corresponds to the curvature of the logarithmic spiral for reflection angles of which cos 6 equals 0.9.

3,439,163 5 6 4. An X-ray crystal monochromator as claimed in OTHER REFERENCES claim 2, in which the monochromator is constituted of High Intensity X ray Monochromator by P. Kirk a carrier of metal coated with a thin layer of a subsance Patrick from Review of Scientific Instruments, VOL wh1ch reflects X-rays.

12, November 1941, pp. 552-554.

References Cited WILLIAM F. LINDQUIST, Primary Examiner. UNITED STATES PATENTS U.S. Cl. X.R. 2,853,617 9/1958 Berreman 250-515 250-53 

